It appears that lately iTunes and the App Store login pages are not working properly with oldest obsolete operating systems. I've been seeing complaints from users running El Capitan, Sierra and High Sierra about their inability to properly login and use those applications - iTunes and the App Store.
There have also been some with trouble using Mojave, but sometime that one still works.
Keep your eyes on the forums here, maybe do search for iTunes access or App Store access with El Capitan and see what other info you might find.
The problem is about the security and the protocols the obsolete browsers can't use to access those services.
I wouldn't hold my breath waiting for Apple to fix the problem.